When operated on a vehicle, tire/wheel assemblies sometimes cause annoying vibrations even when they are properly balanced. Complaints concerning such vibration are a costly source of warranty claims made against vehicle manufacturers.
The tendency to cause such vibration arises from at least three sources; structural nonuniformities inherent in the construction of tires, dimensional nonuniformities, particularly radial runout, in wheels and the manner in which the tire and wheel nonuniformities interact with one another. As will become clear, those interactions tend to either add or, preferably, cancel depending on the orientation of the tire with respect to the wheel. As the present invention recognizes, the net degree of such cancellation which can be effected for given populations of tires and wheels also depends importantly upon the manner in which individual tires and wheels are selectively paired. Previous efforts to limit vibration have been directed toward reducing the contributions of all of the above three sources but have focused principally on ensuring that tires and wheels as individual components are as uniform as possible and on orienting the tires and wheels to effect cancellation. However, prior art proposals for pairing tires and wheels in order to maximize cancellation are impractical to implement on a production scale. Moreover, they do not offer optimum performance.
Tire manufacturers typically employ tire uniformity inspection machines to make force variation measurements which characterize the uniformity of construction of tires and thus, their tendency to cause vibration in various directions. Such machines operate by measuring the magnitude and angular orientation of reaction forces generated by the tire along various axes of interest as the tire rolls against the surface of a load wheel under a controlled radial load.
In a typical tire uniformity inspection machine, tires are fed by conveyor to a test station where each tire is mounted upon a chuck, inflated and rotatably driven with its tread surface in forced contact with the circumferential surface of the load wheel. The load wheel rotates on a spindle which is supported on each end by an array of load cells which measure forces acting on the load wheel in directions of interest including the radial direction. To do so, a rotary encoder coupled to the chuck tracks the rotation of the tire by generating a series of equiangularly spaced pulses as the tire rotates. Those pulses, together with the outputs of the load cells, are communicated to a computer associated with the machine. In response to the pulses, the computer samples and stores measurements of the instantaneous force waveforms generated by the load cells in each direction of interest over a complete revolution of the tire. The computer carries out Fourier analysis of those measurements in order to resolve them into harmonic components including the first harmonic and selected higher order harmonics. Each harmonic is conventionally represented in vector form as a magnitude and an angle. The angle of the vector identifies a particular angular location on the tire whereat the highpoint of the harmonic component occurs. Tire uniformity inspection machines commonly include facilities for marking the sidewall of the tire under test at that particular angular location for a specified harmonic, typically the first harmonic. Tires whose force variation values or harmonics thereof exceed desired magnitude limits can then be rejected or subjected to a grinding operation in attempt to correct the problem. However, as noted above, the overall tendency of a tire/wheel assembly to give rise to vibration is not determined solely by the lack of structural uniformity in tires. It is also contributed to by dimensional non-uniformity in wheels.
Dimensional nonuniformities in wheels, such as average radial runout, can also be measured and resolved into harmonic components. Radial runout gives rise to radial force variations in a tire/wheel assembly by interacting with the effective spring rate of the tire mounted on the wheel. For example, assume that the radial runout of a given wheel has a highpoint value of .times. (inches) at a particular angular location on the wheel. Further assume that a tire having an effective spring constant in the radial direction of k (pounds per inch) is mounted upon that wheel. Ignoring any force variation due to non-uniformity of the tire, such a combination can be expected to generate a radial force component of k times .times. pounds at that angular location.
Accordingly, it has been the practice in the art to analyze vehicle wheels for dimensional uniformity using wheel uniformity analyzing machines such as the Model SSP-WUA wheel uniformity analyzer manufactured by Akron Standard, an ITW Company to whom the present application is assigned. When equipped with a marking system, such a machine can provide an identifiable mark at a specific location on the circumference of the wheel, such as the circumferential location 180.degree. opposite that of the location corresponding to the angle of the first harmonic of the average radial runout of the wheel.
In a tire/wheel assembly, the harmonics of the radial force variation of the tire and the harmonics of average radial runout characteristics of the wheel (by virtue of the latter's interaction with the spring rate of the tire) combine to produce a resultant force variation harmonics whose magnitudes indicate the tendency of the tire/wheel assembly as a whole to vibrate. It has been known to attempt to minimize vibration of tire/wheel assemblies by orienting the tire with respect to the wheel such that the angular location of the first harmonic of the radial force variation of the tire lies 180.degree. opposite the angular location of the first harmonic of average radial runout of the wheel. When so mounted, the first harmonic of radial force variation of the tire tends to be at least partially cancelled by force component induced by the first harmonic of radial runout of the wheel and vice versa. This helps to reduce the tendency of the tire/wheel assembly to vibrate in the radial direction when in use. However, since only the angles of the respective harmonics are considered, wheels having large average radial runout magnitudes, can often be paired with tires having large radial force variation magnitudes, or vice versa so that the resultant cancellation will be far from complete. On the other hand, if magnitude of the first harmonic of the average radial runout of the wheel, after being multiplied by the effective spring rate of the tire, happens to be of nearly the same magnitude as the corresponding harmonic of tire radial force variation of the tire, the effective cancellation will be nearly perfect, leaving a resultant force variation first harmonic of small magnitude. Even so, it is not practical, particularly on a production scale, to pair tires and wheels by attempting to match each tire with a wheel selected such that the magnitude of a given harmonic of force expected to be induced by the wheel equals, and can therefore precisely cancel, the corresponding force harmonic contributed by the tire. The reason for this will now be explained with reference to FIG. 1.
FIG. 1 is a graph illustrating a hypothetical distribution function of the magnitudes of a parameter, such the first harmonic of radial force variation among a population of tires (A). Graphed on the same coordinates appears a hypothetical distribution function of the magnitudes of a second parameter, such as the first harmonic of the average radial runout among a population of wheels (B) which has been converted to units of force by multiplying by the effective spring rate of tires (A). Because of inherent manufacturing differences, the respective distributions for tires and wheels will usually differ from one another. Ordinarily, by way of illustrative example only and not limiting of the present invention in any way, the distribution of wheel population (B) can generally be expected to be somewhat narrower (i.e., have a lower standard deviation) and have a lower mean value than that of tire population (A). In the tire uniformity inspection procedure, tires whose first harmonic of radial force variation have a magnitude exceeding a predetermined tire reject limit can be automatically rejected thereby truncating the tire distribution by eliminating those tires in region F as illustrated.
By inspection of FIG. 1, it can be appreciated that if one were to attempt to match each tire from population (A) having a first harmonic of radial force variation of a given magnitude with a wheel from population (B) whose first harmonic of average radial runout is expected to give rise to a force of that same given magnitude, only tires and wheels lying in region C, where the tire and wheel distributions overlap, could be so matched. Even rejecting the worst tires from population (A) (i.e., those from region F) does not solve this problem. Once the supplies of tires and wheels within region C were exhausted, there would remain an excess of wheels having disproportionately small first harmonic of average radial runout magnitudes (region D in FIG. 1) and an excess of tires with much larger (region E in FIG. 1). No matter how those remaining tires and wheels were paired, the resulting tire/wheel assemblies would have quite large radial first harmonic resultants. Thus, while portions (region C) of the tire and wheel populations would be extremely well matched so that the first harmonics contributed by the tires would almost perfectly cancel the first harmonics contributed by the wheels, the remaining portions (regions D and E) of the populations would be grossly mismatched due to the lack of suitable mates. As a result, the tire/wheel assemblies produced from the components in regions D and E would have a much greater tendency to vibrate when used on a vehicle.
Although the two curves in FIG. 1 are hypothetical and could vary in size, shape and even relative position, one can appreciate that the above problem would always occur using the pairing technique discussed above, at least to some degree, except in the unlikely event that the two curves happened by chance to completely overlap one another. On the opposite extreme, the tire and wheel distribution curves might be spaced apart and not have any substantial areas of overlap. In that event, little if any pairing by matching the respective magnitudes of corresponding force harmonics contributed by tires and wheels on the other would be possible. Under those circumstances, if tires and wheels from adjacent ends of the two curves were paired, the tires and wheels paired from the opposite ends of the two curves would be severely mismatched:
In addition to the tendency to leave portions of the tire and wheel populations without suitable mates, it is also quite impractical and expensive on a production scale to attempt to pair tires and wheels by individually selecting a wheel such that the measured magnitude of a given harmonic of radial force variation of that tire equals the magnitude of the corresponding radial force harmonic which will be contributed by the radial runout of the wheel through its interaction with the spring rate of the tire. In order to do so, it would be necessary to determine the magnitude of that harmonic for nearly every tire as well as the magnitude of the corresponding harmonic of radial force expected to be contributed by nearly every wheel in the respective populations of tires and wheels prior to making even the first tire/wheel assembly. It would also be necessary to have all or nearly all the tires and wheels physically stored in a readily accessible manner and to maintain records of the magnitudes of their respective force harmonics. Tires and wheels having identical or nearly identical magnitudes would then have to be selected, removed from storage and brought to a tire/wheel assembly station to be mounted in the proper mutual orientation.
Such a technique would impose enormous physical storage and material handling problems which would grow disproportionately as the size of the tire and wheel populations to be accommodated were increased. For example, production runs of tires and wheels numbering the tens or even hundreds of thousands of units are not uncommon. The size, cost and complexity of a system for physically storing such enormous batches of tires and wheels as well as the elaborate equipment which would be needed to select and physically retrieve individual tires and wheels from those enormous batches renders it highly impractical to attempt to pair tires and wheels by individually selecting wheels and tires from large populations of wheels and tires such that the measured magnitude of a given harmonic of radial force variation of each tire equals the magnitude of the corresponding harmonic of radial force expected to be contributed by a particular wheel.